The effects of a random component of the magnetocrystalline anisotropy on the magnetic properties and critical behavior of DyAl$\sb2$ have been investigated using bulk magnetic measurements. Randomness in the magnetic anisotropy is brought about by site diluting ferromagnetic DyAl$\sb2$ with the non-magnetic, isomorphic intermetallic YAl$\sb2$. Dilution causes a distortion of the cubic Laves phase unit cell because of the lattice mismatch between DyAl$\sb2$ and YAl$\sb2$, and lowers the local crystal symmetry. This effect induces a random component of the magnetic anisotropy and causes the local easy axis of magnetization to vary in direction from site to site. Additional contributions come from differences in charge screening that exist between Dy and Y, from spin-orbit scattering by the conduction electrons, and from anisotropic exchange and dipolar interactions that occur when a Dy ion is substituted with non-magnetic Y.Low field thermal scans of the bulk magnetization show no sign of a kink point which would indicate a divergent susceptibility for concentrations 0.10 $\leq$ $x$ $\leq$ 0.80, and thus the presence of a spontaneous moment. However, a significant increase in the magnetization occurs at a temperature $T\sb{c}$ which increases with Dy concentration. The magnetization data at high temperatures $T$ $\gg$ $T\sb{c}$ are well described by a Curie-Weiss law. The paramagnetic Curie temperatures are positive, indicating an average ferromagnetic exchange coupling between Dy ions, and increase with $x$. The paramagnetic moment shows no evidence of quenching across the series, and confirms the well localized nature of the 4f electronic orbitals.Hysteresis loops display very small coercive fields and remanence, which are suggestive of weak random magnetic anisotropy (RMA). Arrott plots are qualitatively similar to the predictions of Aharony and Pytte in that isotherms exhibit anomalous curvature at low fields which changes sign across the transition temperature, and no long-range magnetic order up to $x$ = 0.80. A ferromagnetic scaling analysis applied to the line of transitions at $T\sb{c}$ resulted in a surprisingly good collapse of the magnetization data. Values for $\delta$ obtained from this analysis are independent of $x$ up to $x$ = 0.90, and close to the Aharony and Pytte value of 7/3.